Design and implement algorithms to solve a complex multi-objective optimization problem with conflicting objectives and non-linear constraints. Your solution should include: (1) mathematical formulation of the problem; (2) discussion of Pareto optimality concepts; (3) implementation of at least three different approaches (e.g., weighted sum method, epsilon-constraint method, evolutionary algorithms); (4) handling of constraints through penalty functions or other methods; (5) convergence criteria and stopping conditions; (6) visualization of Pareto front; (7) quantitative comparison of methods using appropriate metrics; (8) sensitivity analysis of parameters. Discuss computational complexity and potential improvements.